Over the years, people have tried to say that the Star of Bethlehem was a supernova, a comet, or the latest popular notion -- a triple conjunction of Jupiter and the star Regulus.  Let's consider each of these:

Supernova 

From time to time in history, a nova was seen in the night sky, a "new star," from the Latin word for "new."  Modern science defines a supernova as an exploding star, which shines very brightly for a short time and then goes away.  Throughout history, a number of novae have been observed in the night sky.  Ancient Chinese astronomers kept a careful record of such new stars, though no such records survive in any Greek, Roman, or other western sources. 

It would be very tempting to suppose the Star of Bethlehem would have been a supernova.  Such a unique occurrence is very rare and would be a very conspicuous sign in the sky that would attract a lot of attention.  The problem is, there is no historical or scientific evidence of such a supernova.  The Chinese did not record any new stars within the suitable period of time.  

Also, supernovae leave behind a remnant in the form of a nebula that can be seen through telescopes on the Earth.  The most famous example is the Crab Nebula in the constellation Taurus, the remnant of a supernova that the Chinese observed in A.D. 1054.  If there were a supernova that was visible over the latitude of Bethlehem in or around 4 B.C., a remnant nebula should be visible in a certain region of the sky.  However, no such object can be found.

Triple Conjunction of Jupiter and Regulus

One theory that has been popular in recent years is the notion that the Star of Bethlehem was a very rare triple conjunction of the bright planet Jupiter with the star Regulus in the constellation Leo.  In this astronomical event, Jupiter would have had a retrogradation in Leo such that it would have passed this bright star three times.  This theory is compelling in that it is full of astrological symbolism that might indicate to a Persian magus that a king was born in Judaea. 

Such a triple conjunction event did actually occur over a span from September, 3 B.C. through May, 2 B.C.  Blazingly bright Jupiter, which signifies kingship, passed three times very closely to the brightest star of Leo, which might signify Judah (as from the Blessing of Israel, Genesis 49:9).  No doubt this was at least a spectacular sight to anyone who saw it at the time.  A planetary alignment similar to this was depicted in the recent movie, The Nativity Story

The triple conjunction theory makes the rounds every Christmas, and is  explained in detail in a DVD from http://www.bethlehemstar.net/.  Though a compelling case is made, this triple conjunction event is not a "star" per se (astera, as stated in the Greek text of Matthew 2:2) but rather an alignment of a well known star and planet.  This triple conjunction is a series of close approaches of these objects spread out over an eight month period.  For these reasons, I personally find this to be an unsatisfying explanation to account for the Star of Bethlehem.  

Also, this conjunction series occurs after the traditionally accepted date of the death of Herod in 4 B.C. as suggested by Josephus.  However, scholars are constantly debating over the skimpy facts, so a strong element of guesswork is involved in any of these chronologies or Star theories.